The ATM had tabled a motion of no confidence against president Cyril Ramaphosa.
The move sought to postpone the motion pending the outcome of its court challenge to have the motion conducted by way of secret ballot.
However, Mapisa-Nqakula declined the ATM’s request.
During the sitting, the speaker struggled to hold order as MPs could be heard screaming and speaking over each other.
ATM leader Vuyolwethu Zungula kicked off the session by citing Rule 90 which states no MP may discuss on any case that is before the court.
He said there was ongoing litigation between ATM and the speaker regarding the method of voting and said the matter could not continue today.
“There is a case number which shows there’s an ongoing case. The fact the court said it’s not urgent, doesn’t mean it’s not going forward.
“We can’t proceed with this matter whereas manner of voting is for judicial review. We’re not going to withdraw. In the programming committee, we were told the decision rests with you. As ATM, this motion must be postponed pending court outcome,” he said.
Agreeing with Zungula, EFF deputy president Floyd Shivambu concurred the matter should be postponed until a resolution on the secret ballot had been finalised in court.
“This is being challenged because you refused the secret ballot. Legitimately, the ATM is saying we can’t proceed fairly if we’re not going to be granted the opportunity for a secret ballot because we know once it comes, we’ll split the ANC in half.
“We’ve got the capacity, we did it before. We’ve got the experience in this. It’s a fact the matter is before the court,” Shivambu said.
Wednesday’s motion of no confidence would have been the first time Ramaphosa faced such a motion since becoming president.
Al-Jamaah leader Ganief Hendricks labelled the motion a cheap political stunt aimed at destabilising the country.
“The motion is nothing but a political stunt to destabilise the house and country for political means,” he said.
IFP MP Narend Singh said ATM had indicated they did not want to motion debate on Wednesday but wait till the court process was concluded.
“I’d like to suggest the matter be referred to programming committee on whether matter should remain on the order paper. If it remains, it denies any other party an opportunity to bring back such a motion,” Singh said.
Making a ruling, Mapisa-Nqakula said parliament would be not proceeding with the matter on Wednesday.
“What happens forward will be dealt with tomorrow,” she said.